Missing coin sum

You have $n$ coins, each with a positive integer value. Find the smallest positive sum that cannot be made using each coin at most once.

The first line contains $n$ ($1 \le n \le 2 \cdot 10^5$). The second line contains $n$ integers ($1 \le a_i \le 10^9$).

A single number — the smallest positive sum that cannot be made.

Sort the coins in increasing order. Suppose the first $k$ coins can make every sum from $1$ to $s$. If the next coin is $a \le s + 1$, every sum from $1$ to $s + a$ can now be made. If $a > s + 1$, the sum $s + 1$ can never be made — it is the answer.

In the first example the sorted coins are $1, 2, 2, 7$: $s = 5$ and the next coin $7 > 6$, so the answer is $6$. The answer reaches $2 \cdot 10^{14}$ — a 64-bit type is needed.

Source: CSES, problem 2183, acmp.ru, problem 427.